Optical system



OPTICAL SYSTEM Original Filed May 22, 1941 Patented July 31, 1945 UNITEDSTATES PATENT orrics OPTICAL SYSTEM Original application May 22, 1941,Serial No.

394,709. Divided and this application March 10. 1942, Serial No.434,131. In Great Britain Ma! 12 Claims.

This application is a' division of my copendinK application SerialNumber 394,709, flied May 22, 1941, which has become Patent No.2,363,379, dated December 7, 1943, and the invention relates to opticalsystems for use as optical objectives for various purposes, includingphotographic and projection objectives and microscope and telescopeobjectives. Such objectives have hitherto usually been constituted by asystem of retracting lenses, and serious difliculties' have consequentlyarisen in achieving any refined correction of chromatic aberration Theuse of reflecting surfaces would avoid such difficulties, and thepresent invention has for its object to provide a satisfactory objectivein which the optical power is supplied by curved reflecting surfaces.

In order to correct a concave mirror for spherical aberration it hasbeen usual to make it paraboloidal, but a paraboloidal mirror hasserious uncorrected coma and astigmatism and can only be used inpractice for a very small angular field.

It has recently been discovered that a concave spherical mirror can besimultaneously corrected for spherical aberration, coma and astigmatismby providing in front of the mirror at or near its centre of curvature acorrecting element in the form of a substantially afocal plateconstituted by a deformed plane parallel plate. Such an arrangement isof restricted practical value since the focal surface of the mirror is aspherical surface concentric with the mirror and of half the radiusthereof.

A fin'ther object of the invention is to provide an optical system inwhich the opticalpower is supplied by spherical reflecting surfaces andin which correction is afforded for spherical and chromatic aberrationsand for coma and astigmatlsm with the use of a minimum number ofcorrecting elements. For achieving this object the optical system maycomprise two or more spherical reflecting surfaces having substantiallythe same "equivalent centre of curvature" and means disposed at suchcommon centre for simultaneously correcting. at least to the firstorder, for the spherical aberration, coma and astigmatism of suchreflecting surfaces.

It is to be understood that the phrase "equivalent centre of curvature"is herein used to mean either the geometrical centre of curvature of thesurface or, if there are any intervening elemerits, the image of suchcentre formed by paraxial imagery by such intervening elements.

The correcting means preferably comprise a substantially afocalcorrecting surface intersecting the optical axis substantially at thecommon equivalent centre of curvature of thespherical reflectingsurfaces. Such correcting surface may be paraxially afocal, in whichcase it will consist of a surface of revolution generated by rotationabout the :c-axis (that is the optical axis of the system) of a curve ofthe form a:=Ar +By-ihigher even powers of 11 wherein the coefllcientsALB (which deter mine the extent of deformation of the surface from aplane surface) are such that the surface will correct for the sphericalaberration, coma and stigmatism of the spherical reflecting surfaces. necoeiilcient A, which may be termed the coeiilcient of the first-orderdeformation, is associated with the correction of the first-orderaberrations, and the coefficient B of the secondorder deformation islikewise associated with the correction of the second-order aberrations,and so on. It may be mentioned that the first-order deformation of thesurface will be the algebraic sum of the first-order deformationsrequired for correction of the first-order aberrations of the individualsurfaces, but this relationship does not obtain for the higher orderdeformations.

The afocal correcting surface may be constituted by one-of the surfacesof a plate through which the light is transmitted, or alternatively maybe in the form of a reflecting surface.

The invention may be carried into practice in various ways, but someconvenient arrangements according thereto are diagrammaticallyillustrated in the accompanying drawing, in which Figure 1 illustrates asimple arrangement of optical system which can be used, in conjunctionwith other optical elements, for a\variety of pur- Figures 2 and 3respectively show mcdiflcations of the arrangement of Figure 1,

Figure 4 illustrates the application of the invention to an anastigmaticphotographic objective,

Figure 5 illustrates the application of the invention to a copyingobjective, and

Figure 6 illustrates one practical constructional form for a pair ofreflecting surfaces, as applied by way of example to the arrangement ofFigure 1.

In the arrangement of Figure l, the optical system comprises twoapproximately concentric spherical mirrors and one correcting plate. Thelight after passing through the correcting plate R1 R2 is reflected atone of the mirrors R: which is annular and concave. and then again atthe other mirror R4, which is convex, whence it passes through themiddle of the concave mirror R: to the focal plane F. The correctingplate is thin with its front surface R1 plane, whilst its rear surfaceR2, which intersects the optical axis substantially at the common centreof curvature Ad of the two mirrors R: R4 consists of an afocal surfacedeformed from the true plane to an extent sufilcient to correct for thealgebraic sum of the first order aberrations of the two mirrors. Thusthe rear surface Ra of the plate is slightly convex towards the front,and its position and shape are such that its spherical aberration, comaand astigmatism substantially balance out those of the two mirrors RsR4.

Approximate numerical data for one example of this arrangement,calculated to give correction for the case of an infinitely distantobject, are given in the following table, wherein (as also in thevarious other tables set out below) Ri Rs represent the radius ofcurvature of the individual surfaces counting from the front (thepositive sign indicating that the surface is convex to the front and thenegative that it is concave thereto), and D1: D2: represent thedistances between the vertices Al A2, A: A1 of such surfaces (the minussign where given indicating that the second of the two surfaces is infront of the first).

The equation to the generating curve is given instead of the radius ofcurvature in the case of a correcting surface, the surface beinggenerated by rotation of such curve about the optical axis. The equationis given in Cartesian coordinates with origin at the vertex and with theaxis coincident with the optical axis.

Example I Thickness Radius or air 3m" separation D X Do 0 1. s R; z-=+.4i i-higher order terms D .86 Rs-. 863

Du-. 259 R4. 608

Distance of focal-plane F from R+.w.

Equivalent foal length 1.0.

Figure 2 shows a modification of Figure l giving correction for the caseof a magnification X2, and numerical data are given in the followingtable.

These two examples are both strongly overcorrected for field curvature.Thus, if a paraxially afocal plate is used, the condition for preciseannulment of the Petzval curvature is that the curvatures of the twomirrors should be equal and opposite. It is not, however, possible fortwo concentric surfaces to have equal curvature and there must thereforebe some considerable residual field curvature aberration. Some slightdivergence from strict concentricity or from accurate positioning of thecorrecting surface at the common centre is, however, sometimesdesirable.

Similar considerations also apply to Example III. which is shown inFigure 3 and of which numerical data are given below, this examplediffering from the first two examples primarily in the order in whichthe light is incident on the surfaces. Thus in this case the light isfirst reflected at the convex mirror R1 and then by the concave mirrorR: before passing the correcting plate R3 R4 to the focal plane F.

R4 z=+.0625 y +higher order terms. Distance oi focal Plane F fromXvi-1.0. Equivalent focal engthLo.

The foregoing arrangements may be modified to employ a reflectingcorrecting surface ,in place of the transmitting correcting plate, andan example of such modification will be described below with referenceto Example IV.

It has already been mentioned that a simple system employing twosubstantially concentric spherical mirrors and a single correctingsurface will of necessity be strongly over-corrected for the fieldcurvature aberration. Such a system will therefore seldom be of muchpractical utility by itselft, but it finds useful practical applicationin combination with other optical elements, for example with elementsunder-corrected for field curvature. Thus for instance the system may beemployed in combination with other spherical reflecting surfaces(appropriately corrected in accordance with the present invention orotherwise) to form an anastigmatic photographic or projection objectivehaving a substantially fiat image fleld. Such an arrangement would beclosely analogous to some of the arrangements described in thespecification of the present applicants copending United States ofAmerica patent application Serial No. 394,709, from which the presentapplication has been divided and would have the advantage of reducingthe number of correcting surfaces employed therein. Again the system canbe combined with other elements to form a copying objective, or canconstitute part of the complete optical system of a telescope ormicroscope.

Thus for instance the system can be usefully applied as a low powertelescope objective in combination with a suitable eyepiece havingundercorrected field curvature and free from astigmatism. The system canalso be used as an erector between an objective and an eyepiece in atelescope, the over-correction of the field curvature balancing the sumof the under-corrections of the objective and the eyepiece, so as toproduce assess? a fiat image field. Again, if the spherical'aber-j*fculated to correct for higher order aberrations ration, coma andastigmatism of the systemare- .-.l.'also correctedior a specifiedniagnificationrsay 25x or 50X, the system can be used as. a; .-i nicroscope objective .in combination with a; s11itable--"eye'-'f piecehaving as ,under-corrected-curvedfield free 1 from astigmatism. Anotherapplication-T'ofthe system is -as part of a fiat-field microscope ob,-

member of very high aperture.

'jective in combination with an under-corrected Example IV, which isshown in Figure and I of which numerical data-are given below, isintended more especially for .useas an anastigmatic objective forphotographic purposes,- butis also suitable as a projection objectiveor-as atelescope objective: This example employsthreesphericalreflecting surfaces and two correcting elements, one of which transznitsthe light whilst the other reflects it. Thus the light, after passingthrough the first correcting element R1 R2, is reflected in turn at aconvex spherical surface R: and two annular concave spherical surfacesR4 R5, after which it is again refiected'at the reflecting correctingsurface'Re before passing to the focal plane F.

Example IV R z== .O200 uH-higher order terms. Distance of focal plane Ffrom Rel-.685. Equivalent focal length 1.000.

Example V flhickness Reirac- AbbV Radius or separativeindcx numtion-l 1)bet Dir-.2925 R3+1.170 D1: .9750 R; :t=-'-.1117 1l'.03844 1/ Du .04031.613 59.3 1 R4 oo 4 D4: .1450

R6 w Dru .0403 1.613 59.3 Re z=+.l117 1/ +.03844 11+ D01 .9750 R --l.l70

Dn-.2925 Ra-1.170

Distance of object plane 0 in front cl R .585. Distance of image plane Ibehind R! .585. Equivalent focal length 1.000.

paraxial image in the spherical mirror R2 of the centre of the sphericalmirror R1, and its deformation correctsfor the aberrations .of themirrors R1 and R7, whilst the deformation "of the surface ,Ra likewisecorrects for the aberrations of the spherical mirrors R2 and Re. The sumof the curvatures of the convergent surfaces R and Rris equal to the sumof the curvatures of the divergent surfacesRi and Re, so that the'objective givesan image'field fiat to the firstorder.

This example gives correction for all aberrations, including distortion,not only to the first. order,

but also to higher orders. The arrangement has,

been calculated for unit magnification-copying,

In this example it willbe seen that;the surfaces T R3 and R4 are;approximately concentric, with their common centre C about .8515, behindR5. It

can readily be shown that the paraxial image Re formed by R5 is'approximatelyfat this common centre C. The.- reflecting. correctingsurfaceIRs is thus approximatelyin thefcorrectv position forsimultaneous correction" of; the. aberrations .of Re and R4, anditsdeformation ,is' such as, to effect sidual field curvature, and itmay benoted that this example has been designed not only to obtaincorrection for first order aberrations, but also to reduce higher orderspherical aberration terms with a view to obtaining an-increasedaperture.

As hasbeen mentioned, the optical system according to the inventioncan'be employed as part of a copying objective, .and numerical data foran example of this (shown in- Figure 5) are given in the table below.This example, which is intended for equal scale copying,consi'sts of asymmetrical arrangement of two optical systems according to 1 theinvention the two correcting usrfaces being ing magnifications;

'd'ata can remain unalter'ed.

butcan readily be modified for other .usualcopy- If desired, the tworecting plates can be combined together-into a single plate, whose twofaces are shaped to constitute the two correcting. surfaces R3 and Rc.,.With a plategof v axial thickness ,314, the other numerical -'T.It-will1be appreciated that the foregoing arrangements have beendescribed by way of example only and maybe modified in various wayswithin the scope of the invention. Thusfor instance thenumericalexamples given above: have been calculated for the m'ost partto correct for first orderaberrations only, and some modificatimes willbe required when higher order terms are considered. Such modificationswill however usually involve only relatively slight numerical I changeswithout any material alteration in the disposed-between the two pairs ofsphericalmir- .rors. The light is-first refiected'at a convex mir.'-.

ror R1 and then at'an annular, concave mirror.

. R2, whence after passing through the twocorrecting plates R3 R1 andfRsRsit is'reflectedin 1 turn at an annular concave mirror Ru and at aconvex mirror Ra. This example has been calarrangement of the objective.

Again the various reflecting surfaces in the foregoing examples'havebeenseparated by air gaps, but it will be' appreciated that they may, ifdesired, be formed as internally reflecting surfaces. Thus, forinstance, as shown in Figure 6, the two spherical mirrors of Figure 1can be formed as internally reflecting surfaces on a single piece ofglass, having a plane annular entrance surface B'na concave sphericalannular internally reflecting surface B2 (corresponding to the surfaceR3 of Figure 1), a convex spherical internally reflecting surface Ba(corresponding to "the surface Riof l's'igure 1) and an exit surface Bl,which may be (as shown) spherical and concentric with the; axial focalpoint of the system or may beplanflwithin and adjacent to the an- 1nular surface Bil The two internally reflectin surfaces are preferablymetallised.

What I claim as my invention and desire to secure by Letters Patent is:

1. An, optical system including a plurality of axially aligned sphericalreflecting surfaces having substantially the same equivalent centre ofcurvature, and means disposed substantially at such common centre. forsimultaneous correcting for the sphericalaberration, coma andastigmatism of such surfaces.

2. An optical system as claimed in claim 1, in which the correctingmeans. comprises a substantially afocal correcting surface.

3. An optical system as claimed in claim 1, in which the correctingmeans comprises a substantially afocal correcting surface constituted byone of the surfaces of a plate through which the light is transmitted.

4. An optical system as claimed in claim 1, in which the correctingmeans comprises a substantially afocal correcting surface in the form ofa reflecting surface.

5. An optical system as claimed in claim 1, in which the correctingmeans comprises a substantially afocal correcting surface constituted bya surface of revolution generated by rotation about the m-axis (that isthe optical axis of the system) of a curve of the form (in Cartesiancoordinates :c, y)

ZI +BZI +higher even powers ofy wherein the coefficients A-B (whichdetermine the extent of deformation of the surface from a planesurface)are. such that the surface will correct for the spherical aberration,coma .and astigmatism of the associated spherical refleeting surfaces.

6. An optical objective comprising three axially aligned sphericalreflecting surfaces of which two are convergent and one divergent, twoof such surfaces having the same equivalent centre of curvature, asubstantially afocal correcting surface intersecting the optical axissubstantially at such common centre and acting to correct simultaneouslyfor the spherical aberration, coma and astigmatism of the two associatedspherical surfaces and a second substantially afocal correcting surfacefor correcting for the spherical aberration, coma and astigmatism of thethird spherical surface.

7. An optical objective as claimed in claim 6, in which the first afocalcorrecting surface is in the form of a reflecting surface, and thesecond afocal correcting surface is constituted by one of the surfacesof a plate through which the light is transmitted the opposite surfacesof such plate being plane.

8. Anopticalobjective comprising two pairs of axially aligned sphericalreflecting surfaces, the two surfaces of each pair having substantiallythe same equivalent centre of curvature, and two substantially afocalcorrecting surfaces respectively disposed substantially at such twocommon centres, and each acting to correct for the spherverzent.

10. An optical objective as claimed in claim 9.

in which the two afocal correcting surfaces are each constituted by oneof the surfaces of a plate through which the light is transmitted, theelements of the objective being symmetrically arranged.

11. An optical objective comprising three axially aligned sphericalreflecting surfaces, one substantially afocal reflecting correctingsurface, and one substantially afocal correcting surface constituted bya plate through which the light is transmitted,- and having numericaldata sub, stantially as set forth in the following table where R1 R2represent the radii of curvature of the individual surfaces (thepositive sign indicating that the surface is convex to the front and thenegative sign that it is concave thereto), the equations to thegenerating curves being given in place of the radii in the case of thecorrecting surfaces, and Di: D23 represent the axial R a:= .0200 u-i-higher order terms. Distance of focal plane F from Rel-.085.Equivalent focal length 1.000.

12. An optical objective comprising four axially aligned sphericalreflecting surfaces and two substantially afocal correcting surfaceseach constituted by one surface of a plate through which the light istransmitted, and having numerical data substantially as set forth in thefollowing table where R1 R2 represent the radii of curvature of theindividual surfaces (the positive sign indicating that the surface isconvex to the front and the negative sign that it is concave thereto),

the equations to the generating curves being given in place of the radiiin the case of the correcting surfaces, and D12 D23 represent the axialseparations between the individual surfaces:

Distance of object plane 0 in front of 12 ,585. Distance of image planeI behind R .585. Equivalent focal length 1.000.

ARTHUR WARMISHAM.

Thickness Refrac- I Abb V Radius or separative tion index no numberRH-l.

D a-. 2925 R:+1. 170.

D7: 9750 R; I= 1117 ii -.0384! 1;"-

D4 1450 Rt 00 Dan 1 0403 1. 613 59. 3 R 'I=+. 1117 11 03844 1/+ 177 2925Ru-ll 170 v

